Identifier
-
Mp00066:
Permutations
—inverse⟶
Permutations
Mp00159: Permutations —Demazure product with inverse⟶ Permutations
Mp00209: Permutations —pattern poset⟶ Posets
St001964: Posets ⟶ ℤ
Values
[1] => [1] => [1] => ([],1) => 0
[1,2] => [1,2] => [1,2] => ([(0,1)],2) => 0
[2,1] => [2,1] => [2,1] => ([(0,1)],2) => 0
[1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3) => 0
[1,3,2] => [1,3,2] => [1,3,2] => ([(0,1),(0,2),(1,3),(2,3)],4) => 0
[2,1,3] => [2,1,3] => [2,1,3] => ([(0,1),(0,2),(1,3),(2,3)],4) => 0
[2,3,1] => [3,1,2] => [3,2,1] => ([(0,2),(2,1)],3) => 0
[3,1,2] => [2,3,1] => [3,2,1] => ([(0,2),(2,1)],3) => 0
[3,2,1] => [3,2,1] => [3,2,1] => ([(0,2),(2,1)],3) => 0
[1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 0
[3,2,4,1] => [4,2,1,3] => [4,3,2,1] => ([(0,3),(2,1),(3,2)],4) => 0
[3,4,1,2] => [3,4,1,2] => [4,3,2,1] => ([(0,3),(2,1),(3,2)],4) => 0
[3,4,2,1] => [4,3,1,2] => [4,3,2,1] => ([(0,3),(2,1),(3,2)],4) => 0
[4,1,3,2] => [2,4,3,1] => [4,3,2,1] => ([(0,3),(2,1),(3,2)],4) => 0
[4,2,3,1] => [4,2,3,1] => [4,3,2,1] => ([(0,3),(2,1),(3,2)],4) => 0
[4,3,1,2] => [3,4,2,1] => [4,3,2,1] => ([(0,3),(2,1),(3,2)],4) => 0
[4,3,2,1] => [4,3,2,1] => [4,3,2,1] => ([(0,3),(2,1),(3,2)],4) => 0
[1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[3,4,2,5,1] => [5,3,1,2,4] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[3,4,5,1,2] => [4,5,1,2,3] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[3,4,5,2,1] => [5,4,1,2,3] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[3,5,1,4,2] => [3,5,1,4,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[3,5,2,4,1] => [5,3,1,4,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[3,5,4,1,2] => [4,5,1,3,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[3,5,4,2,1] => [5,4,1,3,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[4,2,3,5,1] => [5,2,3,1,4] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[4,2,5,1,3] => [4,2,5,1,3] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[4,2,5,3,1] => [5,2,4,1,3] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[4,3,2,5,1] => [5,3,2,1,4] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[4,3,5,1,2] => [4,5,2,1,3] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[4,3,5,2,1] => [5,4,2,1,3] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[4,5,1,2,3] => [3,4,5,1,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[4,5,1,3,2] => [3,5,4,1,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[4,5,2,1,3] => [4,3,5,1,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[4,5,2,3,1] => [5,3,4,1,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[4,5,3,1,2] => [4,5,3,1,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[4,5,3,2,1] => [5,4,3,1,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[5,1,3,4,2] => [2,5,3,4,1] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[5,1,4,2,3] => [2,4,5,3,1] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[5,1,4,3,2] => [2,5,4,3,1] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[5,2,3,4,1] => [5,2,3,4,1] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[5,2,4,1,3] => [4,2,5,3,1] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[5,2,4,3,1] => [5,2,4,3,1] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[5,3,1,4,2] => [3,5,2,4,1] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[5,3,2,4,1] => [5,3,2,4,1] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[5,3,4,1,2] => [4,5,2,3,1] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[5,3,4,2,1] => [5,4,2,3,1] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[5,4,1,2,3] => [3,4,5,2,1] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[5,4,1,3,2] => [3,5,4,2,1] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[5,4,2,1,3] => [4,3,5,2,1] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[5,4,2,3,1] => [5,3,4,2,1] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[5,4,3,1,2] => [4,5,3,2,1] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[5,4,3,2,1] => [5,4,3,2,1] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[4,3,5,2,6,1] => [6,4,2,1,3,5] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[4,3,5,6,1,2] => [5,6,2,1,3,4] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[4,3,5,6,2,1] => [6,5,2,1,3,4] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[4,3,6,1,5,2] => [4,6,2,1,5,3] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[4,3,6,2,5,1] => [6,4,2,1,5,3] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[4,3,6,5,1,2] => [5,6,2,1,4,3] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[4,3,6,5,2,1] => [6,5,2,1,4,3] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[4,5,2,3,6,1] => [6,3,4,1,2,5] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[4,5,2,6,1,3] => [5,3,6,1,2,4] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[4,5,2,6,3,1] => [6,3,5,1,2,4] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[4,5,3,2,6,1] => [6,4,3,1,2,5] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[4,5,3,6,1,2] => [5,6,3,1,2,4] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[4,5,3,6,2,1] => [6,5,3,1,2,4] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[4,5,6,1,2,3] => [4,5,6,1,2,3] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[4,5,6,1,3,2] => [4,6,5,1,2,3] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[4,5,6,2,1,3] => [5,4,6,1,2,3] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[4,5,6,2,3,1] => [6,4,5,1,2,3] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[4,5,6,3,1,2] => [5,6,4,1,2,3] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[4,5,6,3,2,1] => [6,5,4,1,2,3] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[4,6,1,3,5,2] => [3,6,4,1,5,2] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[4,6,1,5,2,3] => [3,5,6,1,4,2] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[4,6,1,5,3,2] => [3,6,5,1,4,2] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[4,6,2,3,5,1] => [6,3,4,1,5,2] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[4,6,2,5,1,3] => [5,3,6,1,4,2] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[4,6,2,5,3,1] => [6,3,5,1,4,2] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[4,6,3,1,5,2] => [4,6,3,1,5,2] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[4,6,3,2,5,1] => [6,4,3,1,5,2] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[4,6,3,5,1,2] => [5,6,3,1,4,2] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[4,6,3,5,2,1] => [6,5,3,1,4,2] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[4,6,5,1,2,3] => [4,5,6,1,3,2] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[4,6,5,1,3,2] => [4,6,5,1,3,2] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[4,6,5,2,1,3] => [5,4,6,1,3,2] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[4,6,5,2,3,1] => [6,4,5,1,3,2] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[4,6,5,3,1,2] => [5,6,4,1,3,2] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[4,6,5,3,2,1] => [6,5,4,1,3,2] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[5,2,4,3,6,1] => [6,2,4,3,1,5] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[5,2,4,6,1,3] => [5,2,6,3,1,4] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[5,2,4,6,3,1] => [6,2,5,3,1,4] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[5,2,6,1,4,3] => [4,2,6,5,1,3] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[5,2,6,3,4,1] => [6,2,4,5,1,3] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[5,2,6,4,1,3] => [5,2,6,4,1,3] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[5,2,6,4,3,1] => [6,2,5,4,1,3] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[5,3,4,2,6,1] => [6,4,2,3,1,5] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[5,3,4,6,1,2] => [5,6,2,3,1,4] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[5,3,4,6,2,1] => [6,5,2,3,1,4] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[5,3,6,1,4,2] => [4,6,2,5,1,3] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[5,3,6,2,4,1] => [6,4,2,5,1,3] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
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Description
The interval resolution global dimension of a poset.
This is the cardinality of the longest chain of right minimal approximations by interval modules of an indecomposable module over the incidence algebra.
This is the cardinality of the longest chain of right minimal approximations by interval modules of an indecomposable module over the incidence algebra.
Map
Demazure product with inverse
Description
This map sends a permutation π to π−1⋆π where ⋆ denotes the Demazure product on permutations.
This map is a surjection onto the set of involutions, i.e., the set of permutations π for which π=π−1.
This map is a surjection onto the set of involutions, i.e., the set of permutations π for which π=π−1.
Map
inverse
Description
Sends a permutation to its inverse.
Map
pattern poset
Description
The pattern poset of a permutation.
This is the poset of all non-empty permutations that occur in the given permutation as a pattern, ordered by pattern containment.
This is the poset of all non-empty permutations that occur in the given permutation as a pattern, ordered by pattern containment.
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